Adaptive Stabilization of the Korteweg-de Vries-Burgers Equation with Unknown Dispersion

Abstract

This paper studies the adaptive control problem of the Korteweg-de Vries-Burgers equation. Using the Lyapunov function method, we prove that the closed-loop system including the parameter estimator as a dynamic component is globally $L^2$ stable. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's lemma which cannot be used in the present situation. The closed-loop system is shown to be well posed.